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   &#160;<span id="projectnumber">3.4.90 (git rev 67eeba6e720c5745abc77ae6c92ce0a44aa7b7ae)</span>
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<div class="title">Half.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// The conversion routines are Copyright (c) Fabian Giesen, 2016.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// The original license follows:</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">// Copyright (c) Fabian Giesen, 2016</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">// All rights reserved.</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">// Redistribution and use in source and binary forms, with or without</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">// modification, are permitted.</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">// &quot;AS IS&quot; AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment">// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">// HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment">// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment">// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment">// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment">// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment">// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment">// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160; </div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160; </div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="comment">// Standard 16-bit float type, mostly useful for GPUs. Defines a new</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="comment">// type Eigen::half (inheriting either from CUDA&#39;s or HIP&#39;s __half struct) with</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="comment">// operator overloads such that it behaves basically as an arithmetic</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="comment">// type. It will be quite slow on CPUs (so it is recommended to stay</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="comment">// in fp32 for CPUs, except for simple parameter conversions, I/O</span></div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="comment">// to disk and the likes), but fast on GPUs.</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160; </div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160; </div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="preprocessor">#ifndef EIGEN_HALF_H</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="preprocessor">#define EIGEN_HALF_H</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160; </div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="preprocessor">#include &quot;../../InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="preprocessor">#include &lt;sstream&gt;</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160; </div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_GPU_FP16) || defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="comment">// When compiling with GPU support, the &quot;__half_raw&quot; base class as well as</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;<span class="comment">// some other routines are defined in the GPU compiler header files</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;<span class="comment">// (cuda_fp16.h, hip_fp16.h), and they are not tagged constexpr</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="comment">// As a consequence, we get compile failures when compiling Eigen with</span></div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="comment">// GPU support. Hence the need to disable EIGEN_CONSTEXPR when building</span></div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;<span class="comment">// Eigen with GPU support</span></div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;<span class="preprocessor">  #pragma push_macro(&quot;EIGEN_CONSTEXPR&quot;</span>)</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="preprocessor">  #undef EIGEN_CONSTEXPR</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;<span class="preprocessor">  #define EIGEN_CONSTEXPR</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="preprocessor">#define F16_PACKET_FUNCTION(PACKET_F, PACKET_F16, METHOD)           \</span></div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="preprocessor">  template &lt;&gt;                                                       \</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;<span class="preprocessor">  EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_UNUSED                \</span></div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="preprocessor">  PACKET_F16 METHOD&lt;PACKET_F16&gt;(const PACKET_F16&amp; _x) {             \</span></div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;<span class="preprocessor">    return float2half(METHOD&lt;PACKET_F&gt;(half2float(_x)));            \</span></div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;<span class="preprocessor">  }</span></div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160; </div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;<span class="keyword">struct </span>half;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160; </div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;<span class="keyword">namespace </span>half_impl {</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160; </div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="comment">// We want to use the __half_raw struct from the HIP header file only during the device compile phase.</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;<span class="comment">// This is required because of a quirk in the way TensorFlow GPU builds are done.</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;<span class="comment">// When compiling TensorFlow source code with GPU support, files that</span></div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="comment">//  * contain GPU kernels (i.e. *.cu.cc files) are compiled via hipcc</span></div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="comment">//  * do not contain GPU kernels ( i.e. *.cc files) are compiled via gcc (typically)</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="comment">// Tensorflow uses the Eigen::half type as its FP16 type, and there are functions that</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;<span class="comment">//  * are defined in a file that gets compiled via hipcc AND</span></div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;<span class="comment">//  * have Eigen::half as a pass-by-value argument AND</span></div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="comment">//  * are called in a file that gets compiled via gcc</span></div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="comment">// In the scenario described above the caller and callee will see different versions</span></div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;<span class="comment">// of the Eigen::half base class __half_raw, and they will be compiled by different compilers</span></div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;<span class="comment">// There appears to be an ABI mismatch between gcc and clang (which is called by hipcc) that results in</span></div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;<span class="comment">// the callee getting corrupted values for the Eigen::half argument.</span></div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;<span class="comment">// Making the host side compile phase of hipcc use the same Eigen::half impl, as the gcc compile, resolves</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="comment">// this error, and hence the following convoluted #if condition</span></div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;<span class="preprocessor">#if !defined(EIGEN_HAS_GPU_FP16) || !defined(EIGEN_GPU_COMPILE_PHASE)</span></div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="comment">// Make our own __half_raw definition that is similar to CUDA&#39;s.</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="keyword">struct </span>__half_raw {</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;<span class="preprocessor">#if (defined(EIGEN_HAS_GPU_FP16) &amp;&amp; !defined(EIGEN_GPU_COMPILE_PHASE))</span></div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  <span class="comment">// Eigen::half can be used as the datatype for shared memory declarations (in Eigen and TF)</span></div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  <span class="comment">// The element type for shared memory cannot have non-trivial constructors</span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  <span class="comment">// and hence the following special casing (which skips the zero-initilization).</span></div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  <span class="comment">// Note that this check gets done even in the host compilation phase, and</span></div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  <span class="comment">// hence the need for this</span></div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  EIGEN_DEVICE_FUNC __half_raw() {}</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw() : x(0) {}</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)</span></div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  <span class="keyword">explicit</span> EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw(numext::uint16_t raw) : x(numext::bit_cast&lt;__fp16&gt;(raw)) {</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  }</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;  __fp16 x;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;  <span class="keyword">explicit</span> EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw(numext::uint16_t raw) : x(raw) {}</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;  numext::uint16_t x;</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;};</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160; </div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;<span class="preprocessor">#elif defined(EIGEN_HAS_HIP_FP16)</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;  <span class="comment">// Nothing to do here</span></div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  <span class="comment">// HIP fp16 header file has a definition for __half_raw</span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;<span class="preprocessor">#elif defined(EIGEN_HAS_CUDA_FP16)</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;<span class="preprocessor">  #if EIGEN_CUDA_SDK_VER &lt; 90000</span></div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    <span class="comment">// In CUDA &lt; 9.0, __half is the equivalent of CUDA 9&#39;s __half_raw</span></div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    <span class="keyword">typedef</span> __half __half_raw;</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;<span class="preprocessor">  #endif </span><span class="comment">// defined(EIGEN_HAS_CUDA_FP16)</span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;<span class="preprocessor">#elif defined(SYCL_DEVICE_ONLY)</span></div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;  <span class="keyword">typedef</span> cl::sycl::half __half_raw;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160; </div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw raw_uint16_to_half(numext::uint16_t x);</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half_raw float_to_half_rtne(<span class="keywordtype">float</span> ff);</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">float</span> half_to_float(__half_raw h);</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160; </div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="keyword">struct </span>half_base : <span class="keyword">public</span> __half_raw {</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base() {}</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base(<span class="keyword">const</span> __half_raw&amp; h) : __half_raw(h) {}</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160; </div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_GPU_FP16)</span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="preprocessor"> #if defined(EIGEN_HAS_HIP_FP16)</span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base(<span class="keyword">const</span> __half&amp; h) { x = __half_as_ushort(h); }</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="preprocessor"> #elif defined(EIGEN_HAS_CUDA_FP16)</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;<span class="preprocessor">  #if EIGEN_CUDA_SDK_VER &gt;= 90000</span></div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base(<span class="keyword">const</span> __half&amp; h) : __half_raw(*(__half_raw*)&amp;h) {}</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="preprocessor">  #endif</span></div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="preprocessor"> #endif</span></div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;};</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160; </div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;} <span class="comment">// namespace half_impl</span></div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160; </div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="comment">// Class definition.</span></div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="keyword">struct </span>half : <span class="keyword">public</span> half_impl::half_base {</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160; </div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  <span class="comment">// Writing this out as separate #if-else blocks to make the code easier to follow</span></div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;  <span class="comment">// The same applies to most #if-else blocks in this file</span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;<span class="preprocessor">#if !defined(EIGEN_HAS_GPU_FP16) || !defined(EIGEN_GPU_COMPILE_PHASE)</span></div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;  <span class="comment">// Use the same base class for the following two scenarios</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;  <span class="comment">// * when compiling without GPU support enabled</span></div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;  <span class="comment">// * during host compile phase when compiling with GPU support enabled</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;  <span class="keyword">typedef</span> half_impl::__half_raw __half_raw;</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="preprocessor">#elif defined(EIGEN_HAS_HIP_FP16)</span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;  <span class="comment">// Nothing to do here</span></div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;  <span class="comment">// HIP fp16 header file has a definition for __half_raw</span></div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;<span class="preprocessor">#elif defined(EIGEN_HAS_CUDA_FP16)</span></div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  <span class="comment">// Note that EIGEN_CUDA_SDK_VER is set to 0 even when compiling with HIP, so</span></div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;  <span class="comment">// (EIGEN_CUDA_SDK_VER &lt; 90000) is true even for HIP!  So keeping this within</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;  <span class="comment">// #if defined(EIGEN_HAS_CUDA_FP16) is needed</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="preprocessor">  #if defined(EIGEN_CUDA_SDK_VER) &amp;&amp; EIGEN_CUDA_SDK_VER &lt; 90000</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    <span class="keyword">typedef</span> half_impl::__half_raw __half_raw;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;<span class="preprocessor">  #endif</span></div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160; </div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half() {}</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160; </div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half(<span class="keyword">const</span> __half_raw&amp; h) : half_impl::half_base(h) {}</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160; </div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_GPU_FP16)</span></div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;<span class="preprocessor"> #if defined(EIGEN_HAS_HIP_FP16)</span></div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half(<span class="keyword">const</span> __half&amp; h) : half_impl::half_base(h) {}</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="preprocessor"> #elif defined(EIGEN_HAS_CUDA_FP16)</span></div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;<span class="preprocessor">  #if defined(EIGEN_CUDA_SDK_VER) &amp;&amp; EIGEN_CUDA_SDK_VER &gt;= 90000</span></div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half(<span class="keyword">const</span> __half&amp; h) : half_impl::half_base(h) {}</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;<span class="preprocessor">  #endif</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;<span class="preprocessor"> #endif</span></div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160; </div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160; </div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;  <span class="keyword">explicit</span> EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half(<span class="keywordtype">bool</span> b)</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;      : half_impl::half_base(half_impl::raw_uint16_to_half(b ? 0x3c00 : 0)) {}</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;  <span class="keyword">explicit</span> EIGEN_DEVICE_FUNC half(T val)</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;      : half_impl::half_base(half_impl::float_to_half_rtne(static_cast&lt;float&gt;(val))) {}</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  <span class="keyword">explicit</span> EIGEN_DEVICE_FUNC half(<span class="keywordtype">float</span> f)</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;      : half_impl::half_base(half_impl::float_to_half_rtne(f)) {}</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160; </div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;  <span class="comment">// Following the convention of numpy, converting between complex and</span></div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;  <span class="comment">// float will lead to loss of imag value.</span></div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> RealScalar&gt;</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  <span class="keyword">explicit</span> EIGEN_DEVICE_FUNC half(std::complex&lt;RealScalar&gt; c)</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;      : half_impl::half_base(half_impl::float_to_half_rtne(static_cast&lt;float&gt;(c.<a class="code" href="namespaceEigen.html#ac74dc920119b1eba45e9218d9f402afc">real</a>()))) {}</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160; </div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;   EIGEN_DEVICE_FUNC <span class="keyword">operator</span> float()<span class="keyword"> const </span>{  <span class="comment">// NOLINT: Allow implicit conversion to float, because it is lossless.</span></div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;    <span class="keywordflow">return</span> half_impl::half_to_float(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  }</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160; </div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_GPU_FP16) &amp;&amp; !defined(EIGEN_GPU_COMPILE_PHASE)</span></div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  EIGEN_DEVICE_FUNC <span class="keyword">operator</span> __half()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    ::__half_raw hr;</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    hr.x = x;</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    <span class="keywordflow">return</span> __half(hr);</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;  }</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;};</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160; </div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;<span class="comment">// TODO(majnemer): Get rid of this once we can rely on C++17 inline variables do</span></div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;<span class="comment">// solve the ODR issue.</span></div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;<span class="keyword">namespace </span>half_impl {</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> = <span class="keywordtype">void</span>&gt;</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;<span class="keyword">struct </span>numeric_limits_half_impl {</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_specialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_signed = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_integer = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_exact = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> has_infinity = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> has_quiet_NaN = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> has_signaling_NaN = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> std::float_denorm_style has_denorm = std::denorm_present;</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> has_denorm_loss = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> std::float_round_style round_style = std::round_to_nearest;</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_iec559 = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;  <span class="comment">// The C++ standard defines this as &quot;true if the set of values representable</span></div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  <span class="comment">// by the type is finite.&quot; Half has finite precision.</span></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_bounded = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> is_modulo = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> digits = 11;</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> digits10 = 3;      <span class="comment">// according to http://half.sourceforge.net/structstd_1_1numeric__limits_3_01half__float_1_1half_01_4.html</span></div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> max_digits10 = 5;  <span class="comment">// according to http://half.sourceforge.net/structstd_1_1numeric__limits_3_01half__float_1_1half_01_4.html</span></div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> radix = std::numeric_limits&lt;float&gt;::radix;</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> min_exponent = -13;</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> min_exponent10 = -4;</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> max_exponent = 16;</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> max_exponent10 = 4;</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> traps = std::numeric_limits&lt;float&gt;::traps;</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;  <span class="comment">// IEEE754: &quot;The implementer shall choose how tininess is detected, but shall</span></div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;  <span class="comment">// detect tininess in the same way for all operations in radix two&quot;</span></div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> tinyness_before = std::numeric_limits&lt;float&gt;::tinyness_before;</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160; </div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::half (min)() { <span class="keywordflow">return</span> Eigen::half_impl::raw_uint16_to_half(0x0400); }</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::half lowest() { <span class="keywordflow">return</span> Eigen::half_impl::raw_uint16_to_half(0xfbff); }</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::half (max)() { <span class="keywordflow">return</span> Eigen::half_impl::raw_uint16_to_half(0x7bff); }</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::half epsilon() { <span class="keywordflow">return</span> Eigen::half_impl::raw_uint16_to_half(0x1400); }</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::half round_error() { <span class="keywordflow">return</span> Eigen::half_impl::raw_uint16_to_half(0x3800); }</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::half infinity() { <span class="keywordflow">return</span> Eigen::half_impl::raw_uint16_to_half(0x7c00); }</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::half quiet_NaN() { <span class="keywordflow">return</span> Eigen::half_impl::raw_uint16_to_half(0x7e00); }</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::half signaling_NaN() { <span class="keywordflow">return</span> Eigen::half_impl::raw_uint16_to_half(0x7d00); }</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;  <span class="keyword">static</span> EIGEN_CONSTEXPR Eigen::half denorm_min() { <span class="keywordflow">return</span> Eigen::half_impl::raw_uint16_to_half(0x0001); }</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;};</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160; </div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::is_specialized;</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::is_signed;</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::is_integer;</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::is_exact;</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::has_infinity;</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::has_quiet_NaN;</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::has_signaling_NaN;</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> std::float_denorm_style numeric_limits_half_impl&lt;T&gt;::has_denorm;</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::has_denorm_loss;</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> std::float_round_style numeric_limits_half_impl&lt;T&gt;::round_style;</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::is_iec559;</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::is_bounded;</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::is_modulo;</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_half_impl&lt;T&gt;::digits;</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_half_impl&lt;T&gt;::digits10;</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_half_impl&lt;T&gt;::max_digits10;</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_half_impl&lt;T&gt;::radix;</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_half_impl&lt;T&gt;::min_exponent;</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_half_impl&lt;T&gt;::min_exponent10;</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_half_impl&lt;T&gt;::max_exponent;</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">int</span> numeric_limits_half_impl&lt;T&gt;::max_exponent10;</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::traps;</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;EIGEN_CONSTEXPR <span class="keyword">const</span> <span class="keywordtype">bool</span> numeric_limits_half_impl&lt;T&gt;::tinyness_before;</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;}  <span class="comment">// end namespace half_impl</span></div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;}  <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160; </div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;<span class="keyword">namespace </span>std {</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;<span class="comment">// If std::numeric_limits&lt;T&gt; is specialized, should also specialize</span></div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;<span class="comment">// std::numeric_limits&lt;const T&gt;, std::numeric_limits&lt;volatile T&gt;, and</span></div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;<span class="comment">// std::numeric_limits&lt;const volatile T&gt;</span></div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;<span class="comment">// https://stackoverflow.com/a/16519653/</span></div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;<span class="keyword">class </span>numeric_limits&lt;<a class="code" href="namespaceEigen.html">Eigen</a>::half&gt; : <span class="keyword">public</span> Eigen::half_impl::numeric_limits_half_impl&lt;&gt; {};</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;<span class="keyword">class </span>numeric_limits&lt;const <a class="code" href="namespaceEigen.html">Eigen</a>::half&gt; : <span class="keyword">public</span> numeric_limits&lt;Eigen::half&gt; {};</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;<span class="keyword">class </span>numeric_limits&lt;volatile <a class="code" href="namespaceEigen.html">Eigen</a>::half&gt; : <span class="keyword">public</span> numeric_limits&lt;Eigen::half&gt; {};</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;<span class="keyword">class </span>numeric_limits&lt;const volatile <a class="code" href="namespaceEigen.html">Eigen</a>::half&gt; : <span class="keyword">public</span> numeric_limits&lt;Eigen::half&gt; {};</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;}  <span class="comment">// end namespace std</span></div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160; </div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160; </div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;<span class="keyword">namespace </span>half_impl {</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160; </div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;<span class="preprocessor">#if (defined(EIGEN_HAS_CUDA_FP16) &amp;&amp; defined(EIGEN_CUDA_ARCH) &amp;&amp; \</span></div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;<span class="preprocessor">     EIGEN_CUDA_ARCH &gt;= 530) ||                                  \</span></div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;<span class="preprocessor">    (defined(EIGEN_HAS_HIP_FP16) &amp;&amp; defined(HIP_DEVICE_COMPILE))</span></div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;<span class="comment">// Note: We deliberately do *not* define this to 1 even if we have Arm&#39;s native</span></div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;<span class="comment">// fp16 type since GPU halfs are rather different from native CPU halfs.</span></div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;<span class="comment">// TODO: Rename to something like EIGEN_HAS_NATIVE_GPU_FP16</span></div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;<span class="preprocessor">#define EIGEN_HAS_NATIVE_FP16</span></div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160; </div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;<span class="comment">// Intrinsics for native fp16 support. Note that on current hardware,</span></div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;<span class="comment">// these are no faster than fp32 arithmetic (you need to use the half2</span></div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;<span class="comment">// versions to get the ALU speed increased), but you do save the</span></div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;<span class="comment">// conversion steps back and forth.</span></div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160; </div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_NATIVE_FP16)</span></div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;EIGEN_STRONG_INLINE __device__ half operator + (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;<span class="preprocessor">#if defined(EIGEN_CUDA_SDK_VER) &amp;&amp; EIGEN_CUDA_SDK_VER &gt;= 90000</span></div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;  <span class="keywordflow">return</span> __hadd(::__half(a), ::__half(b));</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;  <span class="keywordflow">return</span> __hadd(a, b);</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;}</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;EIGEN_STRONG_INLINE __device__ half <a class="code" href="namespaceEigen.html#a9723b3ff0f2c99fe1081e3eb14380d4c">operator * </a>(<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;  <span class="keywordflow">return</span> __hmul(a, b);</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;}</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;EIGEN_STRONG_INLINE __device__ half operator - (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;  <span class="keywordflow">return</span> __hsub(a, b);</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;}</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;EIGEN_STRONG_INLINE __device__ half operator / (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;<span class="preprocessor">#if defined(EIGEN_CUDA_SDK_VER) &amp;&amp; EIGEN_CUDA_SDK_VER &gt;= 90000</span></div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;  <span class="keywordflow">return</span> __hdiv(a, b);</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;  <span class="keywordtype">float</span> num = __half2float(a);</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;  <span class="keywordtype">float</span> denom = __half2float(b);</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;  <span class="keywordflow">return</span> __float2half(num / denom);</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;}</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;EIGEN_STRONG_INLINE __device__ half operator - (<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;  <span class="keywordflow">return</span> __hneg(a);</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;}</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;EIGEN_STRONG_INLINE __device__ half&amp; operator += (half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;  a = a + b;</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;}</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;EIGEN_STRONG_INLINE __device__ half&amp; operator *= (half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;  a = a * b;</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;}</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;EIGEN_STRONG_INLINE __device__ half&amp; operator -= (half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;  a = a - b;</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;}</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;EIGEN_STRONG_INLINE __device__ half&amp; operator /= (half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;  a = a / b;</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;}</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;EIGEN_STRONG_INLINE __device__ <span class="keywordtype">bool</span> operator == (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;  <span class="keywordflow">return</span> __heq(a, b);</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;}</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;EIGEN_STRONG_INLINE __device__ <span class="keywordtype">bool</span> operator != (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;  <span class="keywordflow">return</span> __hne(a, b);</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;}</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;EIGEN_STRONG_INLINE __device__ <span class="keywordtype">bool</span> operator &lt; (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;  <span class="keywordflow">return</span> __hlt(a, b);</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;}</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;EIGEN_STRONG_INLINE __device__ <span class="keywordtype">bool</span> operator &lt;= (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;  <span class="keywordflow">return</span> __hle(a, b);</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;}</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;EIGEN_STRONG_INLINE __device__ <span class="keywordtype">bool</span> operator &gt; (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;  <span class="keywordflow">return</span> __hgt(a, b);</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;}</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;EIGEN_STRONG_INLINE __device__ <span class="keywordtype">bool</span> operator &gt;= (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;  <span class="keywordflow">return</span> __hge(a, b);</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;}</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160; </div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)</span></div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator + (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;  <span class="keywordflow">return</span> half(vaddh_f16(a.x, b.x));</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;}</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#a9723b3ff0f2c99fe1081e3eb14380d4c">operator * </a>(<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;  <span class="keywordflow">return</span> half(vmulh_f16(a.x, b.x));</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;}</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;  <span class="keywordflow">return</span> half(vsubh_f16(a.x, b.x));</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;}</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;  <span class="keywordflow">return</span> half(vdivh_f16(a.x, b.x));</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;}</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;  <span class="keywordflow">return</span> half(vnegh_f16(a.x));</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;}</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half&amp; operator += (half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;  a = half(vaddh_f16(a.x, b.x));</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;}</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half&amp; operator *= (half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;  a = half(vmulh_f16(a.x, b.x));</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;}</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half&amp; operator -= (half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;  a = half(vsubh_f16(a.x, b.x));</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;}</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half&amp; operator /= (half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;  a = half(vdivh_f16(a.x, b.x));</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;}</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator == (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;  <span class="keywordflow">return</span> vceqh_f16(a.x, b.x);</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;}</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator != (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;  <span class="keywordflow">return</span> !vceqh_f16(a.x, b.x);</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;}</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator &lt; (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;  <span class="keywordflow">return</span> vclth_f16(a.x, b.x);</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;}</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator &lt;= (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;  <span class="keywordflow">return</span> vcleh_f16(a.x, b.x);</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;}</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator &gt; (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;  <span class="keywordflow">return</span> vcgth_f16(a.x, b.x);</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;}</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator &gt;= (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;  <span class="keywordflow">return</span> vcgeh_f16(a.x, b.x);</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;}</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;<span class="comment">// We need to distinguish ‘clang as the CUDA compiler’ from ‘clang as the host compiler,</span></div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;<span class="comment">// invoked by NVCC’ (e.g. on MacOS). The former needs to see both host and device implementation</span></div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;<span class="comment">// of the functions, while the latter can only deal with one of them.</span></div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;<span class="preprocessor">#elif !defined(EIGEN_HAS_NATIVE_FP16) || (EIGEN_COMP_CLANG &amp;&amp; !EIGEN_COMP_NVCC) </span><span class="comment">// Emulate support for half floats</span></div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160; </div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;<span class="preprocessor">#if EIGEN_COMP_CLANG &amp;&amp; defined(EIGEN_CUDACC)</span></div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;<span class="comment">// We need to provide emulated *host-side* FP16 operators for clang.</span></div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;<span class="preprocessor">#pragma push_macro(&quot;EIGEN_DEVICE_FUNC&quot;</span>)</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;<span class="preprocessor">#undef EIGEN_DEVICE_FUNC</span></div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_CUDA_FP16) &amp;&amp; defined(EIGEN_HAS_NATIVE_FP16)</span></div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;<span class="preprocessor">#define EIGEN_DEVICE_FUNC __host__</span></div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;<span class="preprocessor">#else </span><span class="comment">// both host and device need emulated ops.</span></div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;<span class="preprocessor">#define EIGEN_DEVICE_FUNC __host__ __device__</span></div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160; </div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;<span class="comment">// Definitions for CPUs and older HIP+CUDA, mostly working through conversion</span></div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;<span class="comment">// to/from fp32.</span></div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator + (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;  <span class="keywordflow">return</span> half(<span class="keywordtype">float</span>(a) + <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;}</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#a9723b3ff0f2c99fe1081e3eb14380d4c">operator * </a>(<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;  <span class="keywordflow">return</span> half(<span class="keywordtype">float</span>(a) * <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;}</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;  <span class="keywordflow">return</span> half(<span class="keywordtype">float</span>(a) - <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;}</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;  <span class="keywordflow">return</span> half(<span class="keywordtype">float</span>(a) / <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;}</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;  half result;</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;  result.x = a.x ^ 0x8000;</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;  <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;}</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half&amp; operator += (half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;  a = half(<span class="keywordtype">float</span>(a) + <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;}</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half&amp; operator *= (half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;  a = half(<span class="keywordtype">float</span>(a) * <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;}</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half&amp; operator -= (half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;  a = half(<span class="keywordtype">float</span>(a) - <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;}</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half&amp; operator /= (half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;  a = half(<span class="keywordtype">float</span>(a) / <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;}</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator == (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;  <span class="keywordflow">return</span> numext::equal_strict(<span class="keywordtype">float</span>(a),<span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;}</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator != (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;  <span class="keywordflow">return</span> numext::not_equal_strict(<span class="keywordtype">float</span>(a), <span class="keywordtype">float</span>(b));</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;}</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator &lt; (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;  <span class="keywordflow">return</span> float(a) &lt; float(b);</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;}</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator &lt;= (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;  <span class="keywordflow">return</span> float(a) &lt;= float(b);</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;}</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator &gt; (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;  <span class="keywordflow">return</span> float(a) &gt; float(b);</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;}</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">bool</span> operator &gt;= (<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;  <span class="keywordflow">return</span> float(a) &gt;= float(b);</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;}</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160; </div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;<span class="preprocessor">#if defined(__clang__) &amp;&amp; defined(__CUDA__)</span></div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;<span class="preprocessor">#pragma pop_macro(&quot;EIGEN_DEVICE_FUNC&quot;</span>)</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">// Emulate support for half floats</span></div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160; </div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;<span class="comment">// Division by an index. Do it in full float precision to avoid accuracy</span></div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;<span class="comment">// issues in converting the denominator to half.</span></div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (<span class="keyword">const</span> half&amp; a, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> b) {</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;  <span class="keywordflow">return</span> half(<span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(a) / <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(b));</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;}</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160; </div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator++(half&amp; a) {</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;  a += half(1);</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;}</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160; </div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator--(half&amp; a) {</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;  a -= half(1);</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;  <span class="keywordflow">return</span> a;</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;}</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160; </div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator++(half&amp; a, <span class="keywordtype">int</span>) {</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;  half original_value = a;</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;  ++a;</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;  <span class="keywordflow">return</span> original_value;</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;}</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160; </div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator--(half&amp; a, <span class="keywordtype">int</span>) {</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;  half original_value = a;</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;  --a;</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;  <span class="keywordflow">return</span> original_value;</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;}</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160; </div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;<span class="comment">// Conversion routines, including fallbacks for the host or older CUDA.</span></div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;<span class="comment">// Note that newer Intel CPUs (Haswell or newer) have vectorized versions of</span></div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;<span class="comment">// these in hardware. If we need more performance on older/other CPUs, they are</span></div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;<span class="comment">// also possible to vectorize directly.</span></div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160; </div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw raw_uint16_to_half(numext::uint16_t x) {</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;  <span class="comment">// We cannot simply do a &quot;return __half_raw(x)&quot; here, because __half_raw is union type</span></div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;  <span class="comment">// in the hip_fp16 header file, and that will trigger a compile error</span></div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;  <span class="comment">// On the other hand, having anything but a return statement also triggers a compile error</span></div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;  <span class="comment">// because this is constexpr function.</span></div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;  <span class="comment">// Fortunately, since we need to disable EIGEN_CONSTEXPR for GPU anyway, we can get out</span></div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;  <span class="comment">// of this catch22 by having separate bodies for GPU / non GPU</span></div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_GPU_FP16)</span></div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;   __half_raw h;</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;   h.x = x;</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;  <span class="keywordflow">return</span> h;</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;  <span class="keywordflow">return</span> __half_raw(x);</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;}</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160; </div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC numext::uint16_t raw_half_as_uint16(<span class="keyword">const</span> __half_raw&amp; h) {</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;  <span class="comment">// HIP/CUDA/Default have a member &#39;x&#39; of type uint16_t.</span></div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;  <span class="comment">// For ARM64 native half, the member &#39;x&#39; is of type __fp16, so we need to bit-cast.</span></div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;  <span class="comment">// For SYCL, cl::sycl::half is _Float16, so cast directly.</span></div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)</span></div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;  <span class="keywordflow">return</span> numext::bit_cast&lt;numext::uint16_t&gt;(h.x);</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;<span class="preprocessor">#elif defined(SYCL_DEVICE_ONLY)</span></div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;  <span class="keywordflow">return</span> numext::bit_cast&lt;numext::uint16_t&gt;(h);</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;  <span class="keywordflow">return</span> h.x;</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;}</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160; </div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;<span class="keyword">union </span>float32_bits {</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> u;</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;  <span class="keywordtype">float</span> f;</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;};</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160; </div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half_raw float_to_half_rtne(<span class="keywordtype">float</span> ff) {</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;<span class="preprocessor">#if (defined(EIGEN_HAS_CUDA_FP16) &amp;&amp; defined(EIGEN_CUDA_ARCH) &amp;&amp; EIGEN_CUDA_ARCH &gt;= 300) || \</span></div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;<span class="preprocessor">  (defined(EIGEN_HAS_HIP_FP16) &amp;&amp; defined(EIGEN_HIP_DEVICE_COMPILE))</span></div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;  __half tmp_ff = __float2half(ff);</div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;  <span class="keywordflow">return</span> *(__half_raw*)&amp;tmp_ff;</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160; </div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;<span class="preprocessor">#elif defined(EIGEN_HAS_FP16_C)</span></div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;  __half_raw h;</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;<span class="preprocessor">  #if EIGEN_COMP_MSVC</span></div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;    <span class="comment">// MSVC does not have scalar instructions.</span></div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;    h.x =_mm_extract_epi16(_mm_cvtps_ph(_mm_set_ss(ff), 0), 0);</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;<span class="preprocessor">  #else</span></div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;    h.x = _cvtss_sh(ff, 0);</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;<span class="preprocessor">  #endif</span></div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;  <span class="keywordflow">return</span> h;</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160; </div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;<span class="preprocessor">#elif defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)</span></div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;  __half_raw h;</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;  h.x = <span class="keyword">static_cast&lt;</span>__fp16<span class="keyword">&gt;</span>(ff);</div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;  <span class="keywordflow">return</span> h;</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160; </div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;  float32_bits f; f.f = ff;</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160; </div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;  <span class="keyword">const</span> float32_bits f32infty = { 255 &lt;&lt; 23 };</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;  <span class="keyword">const</span> float32_bits f16max = { (127 + 16) &lt;&lt; 23 };</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;  <span class="keyword">const</span> float32_bits denorm_magic = { ((127 - 15) + (23 - 10) + 1) &lt;&lt; 23 };</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> sign_mask = 0x80000000u;</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;  __half_raw o;</div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;  o.x = <span class="keyword">static_cast&lt;</span>numext::uint16_t<span class="keyword">&gt;</span>(0x0u);</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160; </div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> = f.u &amp; sign_mask;</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;  f.u ^= <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a>;</div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160; </div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;  <span class="comment">// NOTE all the integer compares in this function can be safely</span></div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;  <span class="comment">// compiled into signed compares since all operands are below</span></div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;  <span class="comment">// 0x80000000. Important if you want fast straight SSE2 code</span></div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;  <span class="comment">// (since there&#39;s no unsigned PCMPGTD).</span></div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160; </div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;  <span class="keywordflow">if</span> (f.u &gt;= f16max.u) {  <span class="comment">// result is Inf or NaN (all exponent bits set)</span></div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;    o.x = (f.u &gt; f32infty.u) ? 0x7e00 : 0x7c00; <span class="comment">// NaN-&gt;qNaN and Inf-&gt;Inf</span></div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;  } <span class="keywordflow">else</span> {  <span class="comment">// (De)normalized number or zero</span></div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;    <span class="keywordflow">if</span> (f.u &lt; (113 &lt;&lt; 23)) {  <span class="comment">// resulting FP16 is subnormal or zero</span></div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;      <span class="comment">// use a magic value to align our 10 mantissa bits at the bottom of</span></div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;      <span class="comment">// the float. as long as FP addition is round-to-nearest-even this</span></div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;      <span class="comment">// just works.</span></div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;      f.f += denorm_magic.f;</div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160; </div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;      <span class="comment">// and one integer subtract of the bias later, we have our final float!</span></div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;      o.x = <span class="keyword">static_cast&lt;</span>numext::uint16_t<span class="keyword">&gt;</span>(f.u - denorm_magic.u);</div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;    } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;      <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> mant_odd = (f.u &gt;&gt; 13) &amp; 1; <span class="comment">// resulting mantissa is odd</span></div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160; </div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;      <span class="comment">// update exponent, rounding bias part 1</span></div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;      <span class="comment">// Equivalent to `f.u += ((unsigned int)(15 - 127) &lt;&lt; 23) + 0xfff`, but</span></div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;      <span class="comment">// without arithmetic overflow.</span></div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;      f.u += 0xc8000fffU;</div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;      <span class="comment">// rounding bias part 2</span></div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;      f.u += mant_odd;</div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;      <span class="comment">// take the bits!</span></div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;      o.x = <span class="keyword">static_cast&lt;</span>numext::uint16_t<span class="keyword">&gt;</span>(f.u &gt;&gt; 13);</div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;    }</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;  }</div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160; </div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;  o.x |= <span class="keyword">static_cast&lt;</span>numext::uint16_t<span class="keyword">&gt;</span>(<a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> &gt;&gt; 16);</div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;  <span class="keywordflow">return</span> o;</div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;}</div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160; </div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC <span class="keywordtype">float</span> half_to_float(__half_raw h) {</div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;<span class="preprocessor">#if (defined(EIGEN_HAS_CUDA_FP16) &amp;&amp; defined(EIGEN_CUDA_ARCH) &amp;&amp; EIGEN_CUDA_ARCH &gt;= 300) || \</span></div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;<span class="preprocessor">  (defined(EIGEN_HAS_HIP_FP16) &amp;&amp; defined(EIGEN_HIP_DEVICE_COMPILE))</span></div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;  <span class="keywordflow">return</span> __half2float(h);</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;<span class="preprocessor">#elif defined(EIGEN_HAS_FP16_C)</span></div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;<span class="preprocessor">  #if EIGEN_COMP_MSVC</span></div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;    <span class="comment">// MSVC does not have scalar instructions.</span></div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;    <span class="keywordflow">return</span> _mm_cvtss_f32(_mm_cvtph_ps(_mm_set1_epi16(h.x)));</div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;<span class="preprocessor">  #else</span></div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;    <span class="keywordflow">return</span> _cvtsh_ss(h.x);</div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;<span class="preprocessor">  #endif</span></div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;<span class="preprocessor">#elif defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)</span></div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;  <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(h.x);</div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;  <span class="keyword">const</span> float32_bits magic = { 113 &lt;&lt; 23 };</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> shifted_exp = 0x7c00 &lt;&lt; 13; <span class="comment">// exponent mask after shift</span></div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160;  float32_bits o;</div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160; </div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;  o.u = (h.x &amp; 0x7fff) &lt;&lt; 13;             <span class="comment">// exponent/mantissa bits</span></div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160;  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">exp</a> = shifted_exp &amp; o.u;   <span class="comment">// just the exponent</span></div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;  o.u += (127 - 15) &lt;&lt; 23;                <span class="comment">// exponent adjust</span></div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160; </div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;  <span class="comment">// handle exponent special cases</span></div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;  <span class="keywordflow">if</span> (<a class="code" href="namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">exp</a> == shifted_exp) {     <span class="comment">// Inf/NaN?</span></div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;    o.u += (128 - 16) &lt;&lt; 23;    <span class="comment">// extra exp adjust</span></div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code" href="namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">exp</a> == 0) {        <span class="comment">// Zero/Denormal?</span></div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;    o.u += 1 &lt;&lt; 23;             <span class="comment">// extra exp adjust</span></div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;    o.f -= magic.f;             <span class="comment">// renormalize</span></div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;  }</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160; </div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;  o.u |= (h.x &amp; 0x8000) &lt;&lt; 16;    <span class="comment">// sign bit</span></div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;  <span class="keywordflow">return</span> o.f;</div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160;}</div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160; </div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160;<span class="comment">// --- standard functions ---</span></div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160; </div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (<a class="code" href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">isinf</a>)(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;<span class="preprocessor">#ifdef EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC</span></div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160;  <span class="keywordflow">return</span> (numext::bit_cast&lt;numext::uint16_t&gt;(a.x) &amp; 0x7fff) == 0x7c00;</div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160;  <span class="keywordflow">return</span> (a.x &amp; 0x7fff) == 0x7c00;</div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;}</div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (<a class="code" href="namespaceEigen.html#a99adfc5178f3fd5488304284388b2a10">isnan</a>)(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160;<span class="preprocessor">#if (defined(EIGEN_HAS_CUDA_FP16) &amp;&amp; defined(EIGEN_CUDA_ARCH) &amp;&amp; EIGEN_CUDA_ARCH &gt;= 530) || \</span></div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160;<span class="preprocessor">  (defined(EIGEN_HAS_HIP_FP16) &amp;&amp; defined(EIGEN_HIP_DEVICE_COMPILE))</span></div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;  <span class="keywordflow">return</span> __hisnan(a);</div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160;<span class="preprocessor">#elif defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)</span></div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160;  <span class="keywordflow">return</span> (numext::bit_cast&lt;numext::uint16_t&gt;(a.x) &amp; 0x7fff) &gt; 0x7c00;</div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160;  <span class="keywordflow">return</span> (a.x &amp; 0x7fff) &gt; 0x7c00;</div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;}</div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (<a class="code" href="namespaceEigen.html#aba24ec81dec745a00b7f33adead89811">isfinite</a>)(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;  <span class="keywordflow">return</span> !(<a class="code" href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">isinf</a> EIGEN_NOT_A_MACRO (a)) &amp;&amp; !(<a class="code" href="namespaceEigen.html#a99adfc5178f3fd5488304284388b2a10">isnan</a> EIGEN_NOT_A_MACRO (a));</div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;}</div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160; </div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)</span></div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160;  <span class="keywordflow">return</span> half(vabsh_f16(a.x));</div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160;  half result;</div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160;  result.x = a.x &amp; 0x7FFF;</div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160;  <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160;}</div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">exp</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;<span class="preprocessor">#if (EIGEN_CUDA_SDK_VER &gt;= 80000 &amp;&amp; defined EIGEN_CUDA_ARCH &amp;&amp; EIGEN_CUDA_ARCH &gt;= 530) || \</span></div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160;<span class="preprocessor">  defined(EIGEN_HIP_DEVICE_COMPILE)</span></div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160;  <span class="keywordflow">return</span> half(hexp(a));</div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160;   <span class="keywordflow">return</span> half(::expf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160;}</div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#ae7cb2544e4e745bc0067fe793e3f2f81">expm1</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160;  <span class="keywordflow">return</span> half(numext::expm1(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00732"></a><span class="lineno">  732</span>&#160;}</div>
<div class="line"><a name="l00733"></a><span class="lineno">  733</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">log</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00734"></a><span class="lineno">  734</span>&#160;<span class="preprocessor">#if (defined(EIGEN_HAS_CUDA_FP16) &amp;&amp; EIGEN_CUDA_SDK_VER &gt;= 80000 &amp;&amp; defined(EIGEN_CUDA_ARCH) &amp;&amp; EIGEN_CUDA_ARCH &gt;= 530) || \</span></div>
<div class="line"><a name="l00735"></a><span class="lineno">  735</span>&#160;<span class="preprocessor">  (defined(EIGEN_HAS_HIP_FP16) &amp;&amp; defined(EIGEN_HIP_DEVICE_COMPILE))</span></div>
<div class="line"><a name="l00736"></a><span class="lineno">  736</span>&#160;  <span class="keywordflow">return</span> half(::hlog(a));</div>
<div class="line"><a name="l00737"></a><span class="lineno">  737</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00738"></a><span class="lineno">  738</span>&#160;  <span class="keywordflow">return</span> half(::logf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00739"></a><span class="lineno">  739</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00740"></a><span class="lineno">  740</span>&#160;}</div>
<div class="line"><a name="l00741"></a><span class="lineno">  741</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#ac5c8a2cded6b59628f2de04f24d2fff4">log1p</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00742"></a><span class="lineno">  742</span>&#160;  <span class="keywordflow">return</span> half(numext::log1p(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00743"></a><span class="lineno">  743</span>&#160;}</div>
<div class="line"><a name="l00744"></a><span class="lineno">  744</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#a25256faeec3ffd0f3615a0e1e45dfb14">log10</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00745"></a><span class="lineno">  745</span>&#160;  <span class="keywordflow">return</span> half(::log10f(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00746"></a><span class="lineno">  746</span>&#160;}</div>
<div class="line"><a name="l00747"></a><span class="lineno">  747</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#ad2d0241ffaaa3b0b04ec70b59ab066d4">log2</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00748"></a><span class="lineno">  748</span>&#160;  <span class="keywordflow">return</span> half(<span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(EIGEN_LOG2E) * ::logf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00749"></a><span class="lineno">  749</span>&#160;}</div>
<div class="line"><a name="l00750"></a><span class="lineno">  750</span>&#160; </div>
<div class="line"><a name="l00751"></a><span class="lineno">  751</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00752"></a><span class="lineno">  752</span>&#160;<span class="preprocessor">#if (EIGEN_CUDA_SDK_VER &gt;= 80000 &amp;&amp; defined EIGEN_CUDA_ARCH &amp;&amp; EIGEN_CUDA_ARCH &gt;= 530) || \</span></div>
<div class="line"><a name="l00753"></a><span class="lineno">  753</span>&#160;<span class="preprocessor">  defined(EIGEN_HIP_DEVICE_COMPILE)</span></div>
<div class="line"><a name="l00754"></a><span class="lineno">  754</span>&#160;  <span class="keywordflow">return</span> half(hsqrt(a));</div>
<div class="line"><a name="l00755"></a><span class="lineno">  755</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00756"></a><span class="lineno">  756</span>&#160;    <span class="keywordflow">return</span> half(::sqrtf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00757"></a><span class="lineno">  757</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00758"></a><span class="lineno">  758</span>&#160;}</div>
<div class="line"><a name="l00759"></a><span class="lineno">  759</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half pow(<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00760"></a><span class="lineno">  760</span>&#160;  <span class="keywordflow">return</span> half(::powf(<span class="keywordtype">float</span>(a), <span class="keywordtype">float</span>(b)));</div>
<div class="line"><a name="l00761"></a><span class="lineno">  761</span>&#160;}</div>
<div class="line"><a name="l00762"></a><span class="lineno">  762</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#ae6e8ad270ff41c088d7651567594f796">sin</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00763"></a><span class="lineno">  763</span>&#160;  <span class="keywordflow">return</span> half(::sinf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00764"></a><span class="lineno">  764</span>&#160;}</div>
<div class="line"><a name="l00765"></a><span class="lineno">  765</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#ad01d50a42869218f1d54af13f71517a6">cos</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00766"></a><span class="lineno">  766</span>&#160;  <span class="keywordflow">return</span> half(::cosf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00767"></a><span class="lineno">  767</span>&#160;}</div>
<div class="line"><a name="l00768"></a><span class="lineno">  768</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#a3bc116a6243f38c22f851581aa7b521a">tan</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00769"></a><span class="lineno">  769</span>&#160;  <span class="keywordflow">return</span> half(::tanf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00770"></a><span class="lineno">  770</span>&#160;}</div>
<div class="line"><a name="l00771"></a><span class="lineno">  771</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#a0110c233d357169fd58fdf5656992a98">tanh</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00772"></a><span class="lineno">  772</span>&#160;  <span class="keywordflow">return</span> half(::tanhf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00773"></a><span class="lineno">  773</span>&#160;}</div>
<div class="line"><a name="l00774"></a><span class="lineno">  774</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#a6c5c246b877ac331495d21e7a5d51616">asin</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00775"></a><span class="lineno">  775</span>&#160;  <span class="keywordflow">return</span> half(::asinf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00776"></a><span class="lineno">  776</span>&#160;}</div>
<div class="line"><a name="l00777"></a><span class="lineno">  777</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#a3fe3a136370fefae062591304c6a7ebd">acos</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00778"></a><span class="lineno">  778</span>&#160;  <span class="keywordflow">return</span> half(::acosf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00779"></a><span class="lineno">  779</span>&#160;}</div>
<div class="line"><a name="l00780"></a><span class="lineno">  780</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#abf03d773a87830bc7fde51bcd94c89a0">floor</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00781"></a><span class="lineno">  781</span>&#160;<span class="preprocessor">#if (EIGEN_CUDA_SDK_VER &gt;= 80000 &amp;&amp; defined EIGEN_CUDA_ARCH &amp;&amp; EIGEN_CUDA_ARCH &gt;= 300) || \</span></div>
<div class="line"><a name="l00782"></a><span class="lineno">  782</span>&#160;<span class="preprocessor">  defined(EIGEN_HIP_DEVICE_COMPILE)</span></div>
<div class="line"><a name="l00783"></a><span class="lineno">  783</span>&#160;  <span class="keywordflow">return</span> half(hfloor(a));</div>
<div class="line"><a name="l00784"></a><span class="lineno">  784</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00785"></a><span class="lineno">  785</span>&#160;  <span class="keywordflow">return</span> half(::floorf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00786"></a><span class="lineno">  786</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00787"></a><span class="lineno">  787</span>&#160;}</div>
<div class="line"><a name="l00788"></a><span class="lineno">  788</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#aa73e38be0689a463ae14141b9cf89c35">ceil</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00789"></a><span class="lineno">  789</span>&#160;<span class="preprocessor">#if (EIGEN_CUDA_SDK_VER &gt;= 80000 &amp;&amp; defined EIGEN_CUDA_ARCH &amp;&amp; EIGEN_CUDA_ARCH &gt;= 300) || \</span></div>
<div class="line"><a name="l00790"></a><span class="lineno">  790</span>&#160;<span class="preprocessor">  defined(EIGEN_HIP_DEVICE_COMPILE)</span></div>
<div class="line"><a name="l00791"></a><span class="lineno">  791</span>&#160;  <span class="keywordflow">return</span> half(hceil(a));</div>
<div class="line"><a name="l00792"></a><span class="lineno">  792</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00793"></a><span class="lineno">  793</span>&#160;  <span class="keywordflow">return</span> half(::ceilf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00794"></a><span class="lineno">  794</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00795"></a><span class="lineno">  795</span>&#160;}</div>
<div class="line"><a name="l00796"></a><span class="lineno">  796</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#a0211fe61b9e390dfd8ca213fe9c7fca3">rint</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00797"></a><span class="lineno">  797</span>&#160;  <span class="keywordflow">return</span> half(::rintf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00798"></a><span class="lineno">  798</span>&#160;}</div>
<div class="line"><a name="l00799"></a><span class="lineno">  799</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half <a class="code" href="namespaceEigen.html#ad9eaa98e8016ef17024a18a2f3e5bef3">round</a>(<span class="keyword">const</span> half&amp; a) {</div>
<div class="line"><a name="l00800"></a><span class="lineno">  800</span>&#160;  <span class="keywordflow">return</span> half(::roundf(<span class="keywordtype">float</span>(a)));</div>
<div class="line"><a name="l00801"></a><span class="lineno">  801</span>&#160;}</div>
<div class="line"><a name="l00802"></a><span class="lineno">  802</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half fmod(<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00803"></a><span class="lineno">  803</span>&#160;  <span class="keywordflow">return</span> half(::fmodf(<span class="keywordtype">float</span>(a), <span class="keywordtype">float</span>(b)));</div>
<div class="line"><a name="l00804"></a><span class="lineno">  804</span>&#160;}</div>
<div class="line"><a name="l00805"></a><span class="lineno">  805</span>&#160; </div>
<div class="line"><a name="l00806"></a><span class="lineno">  806</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (min)(<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00807"></a><span class="lineno">  807</span>&#160;<span class="preprocessor">#if (defined(EIGEN_HAS_CUDA_FP16) &amp;&amp; defined(EIGEN_CUDA_ARCH) &amp;&amp; EIGEN_CUDA_ARCH &gt;= 530) || \</span></div>
<div class="line"><a name="l00808"></a><span class="lineno">  808</span>&#160;<span class="preprocessor">  (defined(EIGEN_HAS_HIP_FP16) &amp;&amp; defined(EIGEN_HIP_DEVICE_COMPILE))</span></div>
<div class="line"><a name="l00809"></a><span class="lineno">  809</span>&#160;  <span class="keywordflow">return</span> __hlt(b, a) ? b : a;</div>
<div class="line"><a name="l00810"></a><span class="lineno">  810</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00811"></a><span class="lineno">  811</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> f1 = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(a);</div>
<div class="line"><a name="l00812"></a><span class="lineno">  812</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> f2 = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(b);</div>
<div class="line"><a name="l00813"></a><span class="lineno">  813</span>&#160;  <span class="keywordflow">return</span> f2 &lt; f1 ? b : a;</div>
<div class="line"><a name="l00814"></a><span class="lineno">  814</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00815"></a><span class="lineno">  815</span>&#160;}</div>
<div class="line"><a name="l00816"></a><span class="lineno">  816</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (max)(<span class="keyword">const</span> half&amp; a, <span class="keyword">const</span> half&amp; b) {</div>
<div class="line"><a name="l00817"></a><span class="lineno">  817</span>&#160;<span class="preprocessor">#if (defined(EIGEN_HAS_CUDA_FP16) &amp;&amp; defined(EIGEN_CUDA_ARCH) &amp;&amp; EIGEN_CUDA_ARCH &gt;= 530) || \</span></div>
<div class="line"><a name="l00818"></a><span class="lineno">  818</span>&#160;<span class="preprocessor">  (defined(EIGEN_HAS_HIP_FP16) &amp;&amp; defined(EIGEN_HIP_DEVICE_COMPILE))</span></div>
<div class="line"><a name="l00819"></a><span class="lineno">  819</span>&#160;  <span class="keywordflow">return</span> __hlt(a, b) ? b : a;</div>
<div class="line"><a name="l00820"></a><span class="lineno">  820</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00821"></a><span class="lineno">  821</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> f1 = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(a);</div>
<div class="line"><a name="l00822"></a><span class="lineno">  822</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">float</span> f2 = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(b);</div>
<div class="line"><a name="l00823"></a><span class="lineno">  823</span>&#160;  <span class="keywordflow">return</span> f1 &lt; f2 ? b : a;</div>
<div class="line"><a name="l00824"></a><span class="lineno">  824</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00825"></a><span class="lineno">  825</span>&#160;}</div>
<div class="line"><a name="l00826"></a><span class="lineno">  826</span>&#160; </div>
<div class="line"><a name="l00827"></a><span class="lineno">  827</span>&#160;<span class="preprocessor">#ifndef EIGEN_NO_IO</span></div>
<div class="line"><a name="l00828"></a><span class="lineno">  828</span>&#160;EIGEN_ALWAYS_INLINE std::ostream&amp; operator &lt;&lt; (std::ostream&amp; os, <span class="keyword">const</span> half&amp; v) {</div>
<div class="line"><a name="l00829"></a><span class="lineno">  829</span>&#160;  os &lt;&lt; static_cast&lt;float&gt;(v);</div>
<div class="line"><a name="l00830"></a><span class="lineno">  830</span>&#160;  <span class="keywordflow">return</span> os;</div>
<div class="line"><a name="l00831"></a><span class="lineno">  831</span>&#160;}</div>
<div class="line"><a name="l00832"></a><span class="lineno">  832</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00833"></a><span class="lineno">  833</span>&#160; </div>
<div class="line"><a name="l00834"></a><span class="lineno">  834</span>&#160;} <span class="comment">// end namespace half_impl</span></div>
<div class="line"><a name="l00835"></a><span class="lineno">  835</span>&#160; </div>
<div class="line"><a name="l00836"></a><span class="lineno">  836</span>&#160;<span class="comment">// import Eigen::half_impl::half into Eigen namespace</span></div>
<div class="line"><a name="l00837"></a><span class="lineno">  837</span>&#160;<span class="comment">// using half_impl::half;</span></div>
<div class="line"><a name="l00838"></a><span class="lineno">  838</span>&#160; </div>
<div class="line"><a name="l00839"></a><span class="lineno">  839</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00840"></a><span class="lineno">  840</span>&#160; </div>
<div class="line"><a name="l00841"></a><span class="lineno">  841</span>&#160;<span class="keyword">template</span>&lt;&gt;</div>
<div class="line"><a name="l00842"></a><span class="lineno">  842</span>&#160;<span class="keyword">struct </span>random_default_impl&lt;half, false, false&gt;</div>
<div class="line"><a name="l00843"></a><span class="lineno">  843</span>&#160;{</div>
<div class="line"><a name="l00844"></a><span class="lineno">  844</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> half run(<span class="keyword">const</span> half&amp; x, <span class="keyword">const</span> half&amp; y)</div>
<div class="line"><a name="l00845"></a><span class="lineno">  845</span>&#160;  {</div>
<div class="line"><a name="l00846"></a><span class="lineno">  846</span>&#160;    <span class="keywordflow">return</span> x + (y-x) * half(<span class="keywordtype">float</span>(std::rand()) / float(RAND_MAX));</div>
<div class="line"><a name="l00847"></a><span class="lineno">  847</span>&#160;  }</div>
<div class="line"><a name="l00848"></a><span class="lineno">  848</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> half run()</div>
<div class="line"><a name="l00849"></a><span class="lineno">  849</span>&#160;  {</div>
<div class="line"><a name="l00850"></a><span class="lineno">  850</span>&#160;    <span class="keywordflow">return</span> run(half(-1.f), half(1.f));</div>
<div class="line"><a name="l00851"></a><span class="lineno">  851</span>&#160;  }</div>
<div class="line"><a name="l00852"></a><span class="lineno">  852</span>&#160;};</div>
<div class="line"><a name="l00853"></a><span class="lineno">  853</span>&#160; </div>
<div class="line"><a name="l00854"></a><span class="lineno">  854</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span>is_arithmetic&lt;half&gt; { <span class="keyword">enum</span> { value = <span class="keyword">true</span> }; };</div>
<div class="line"><a name="l00855"></a><span class="lineno">  855</span>&#160; </div>
<div class="line"><a name="l00856"></a><span class="lineno">  856</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00857"></a><span class="lineno">  857</span>&#160; </div>
<div class="line"><a name="l00858"></a><span class="lineno">  858</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span>NumTraits&lt;<a class="code" href="namespaceEigen.html">Eigen</a>::half&gt;</div>
<div class="line"><a name="l00859"></a><span class="lineno">  859</span>&#160;    : GenericNumTraits&lt;Eigen::half&gt;</div>
<div class="line"><a name="l00860"></a><span class="lineno">  860</span>&#160;{</div>
<div class="line"><a name="l00861"></a><span class="lineno">  861</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00862"></a><span class="lineno">  862</span>&#160;    IsSigned = <span class="keyword">true</span>,</div>
<div class="line"><a name="l00863"></a><span class="lineno">  863</span>&#160;    IsInteger = <span class="keyword">false</span>,</div>
<div class="line"><a name="l00864"></a><span class="lineno">  864</span>&#160;    IsComplex = <span class="keyword">false</span>,</div>
<div class="line"><a name="l00865"></a><span class="lineno">  865</span>&#160;    RequireInitialization = <span class="keyword">false</span></div>
<div class="line"><a name="l00866"></a><span class="lineno">  866</span>&#160;  };</div>
<div class="line"><a name="l00867"></a><span class="lineno">  867</span>&#160; </div>
<div class="line"><a name="l00868"></a><span class="lineno">  868</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR <span class="keyword">static</span> EIGEN_STRONG_INLINE Eigen::half epsilon() {</div>
<div class="line"><a name="l00869"></a><span class="lineno">  869</span>&#160;    <span class="keywordflow">return</span> half_impl::raw_uint16_to_half(0x0800);</div>
<div class="line"><a name="l00870"></a><span class="lineno">  870</span>&#160;  }</div>
<div class="line"><a name="l00871"></a><span class="lineno">  871</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR <span class="keyword">static</span> EIGEN_STRONG_INLINE Eigen::half dummy_precision() {</div>
<div class="line"><a name="l00872"></a><span class="lineno">  872</span>&#160;    <span class="keywordflow">return</span> half_impl::raw_uint16_to_half(0x211f); <span class="comment">//  Eigen::half(1e-2f);</span></div>
<div class="line"><a name="l00873"></a><span class="lineno">  873</span>&#160;  }</div>
<div class="line"><a name="l00874"></a><span class="lineno">  874</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR <span class="keyword">static</span> EIGEN_STRONG_INLINE Eigen::half highest() {</div>
<div class="line"><a name="l00875"></a><span class="lineno">  875</span>&#160;    <span class="keywordflow">return</span> half_impl::raw_uint16_to_half(0x7bff);</div>
<div class="line"><a name="l00876"></a><span class="lineno">  876</span>&#160;  }</div>
<div class="line"><a name="l00877"></a><span class="lineno">  877</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR <span class="keyword">static</span> EIGEN_STRONG_INLINE Eigen::half lowest() {</div>
<div class="line"><a name="l00878"></a><span class="lineno">  878</span>&#160;    <span class="keywordflow">return</span> half_impl::raw_uint16_to_half(0xfbff);</div>
<div class="line"><a name="l00879"></a><span class="lineno">  879</span>&#160;  }</div>
<div class="line"><a name="l00880"></a><span class="lineno">  880</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR <span class="keyword">static</span> EIGEN_STRONG_INLINE Eigen::half infinity() {</div>
<div class="line"><a name="l00881"></a><span class="lineno">  881</span>&#160;    <span class="keywordflow">return</span> half_impl::raw_uint16_to_half(0x7c00);</div>
<div class="line"><a name="l00882"></a><span class="lineno">  882</span>&#160;  }</div>
<div class="line"><a name="l00883"></a><span class="lineno">  883</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR <span class="keyword">static</span> EIGEN_STRONG_INLINE Eigen::half quiet_NaN() {</div>
<div class="line"><a name="l00884"></a><span class="lineno">  884</span>&#160;    <span class="keywordflow">return</span> half_impl::raw_uint16_to_half(0x7e00);</div>
<div class="line"><a name="l00885"></a><span class="lineno">  885</span>&#160;  }</div>
<div class="line"><a name="l00886"></a><span class="lineno">  886</span>&#160;};</div>
<div class="line"><a name="l00887"></a><span class="lineno">  887</span>&#160; </div>
<div class="line"><a name="l00888"></a><span class="lineno">  888</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00889"></a><span class="lineno">  889</span>&#160; </div>
<div class="line"><a name="l00890"></a><span class="lineno">  890</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_GPU_FP16) || defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)</span></div>
<div class="line"><a name="l00891"></a><span class="lineno">  891</span>&#160;<span class="preprocessor">  #pragma pop_macro(&quot;EIGEN_CONSTEXPR&quot;</span>)</div>
<div class="line"><a name="l00892"></a><span class="lineno">  892</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00893"></a><span class="lineno">  893</span>&#160; </div>
<div class="line"><a name="l00894"></a><span class="lineno">  894</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00895"></a><span class="lineno">  895</span>&#160;<span class="keyword">namespace </span>numext {</div>
<div class="line"><a name="l00896"></a><span class="lineno">  896</span>&#160; </div>
<div class="line"><a name="l00897"></a><span class="lineno">  897</span>&#160;<span class="preprocessor">#if defined(EIGEN_GPU_COMPILE_PHASE)</span></div>
<div class="line"><a name="l00898"></a><span class="lineno">  898</span>&#160; </div>
<div class="line"><a name="l00899"></a><span class="lineno">  899</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00900"></a><span class="lineno">  900</span>&#160;EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool(<a class="code" href="namespaceEigen.html#a99adfc5178f3fd5488304284388b2a10">isnan</a>)(<span class="keyword">const</span> Eigen::half&amp; h) {</div>
<div class="line"><a name="l00901"></a><span class="lineno">  901</span>&#160;  <span class="keywordflow">return</span> (half_impl::isnan)(h);</div>
<div class="line"><a name="l00902"></a><span class="lineno">  902</span>&#160;}</div>
<div class="line"><a name="l00903"></a><span class="lineno">  903</span>&#160; </div>
<div class="line"><a name="l00904"></a><span class="lineno">  904</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00905"></a><span class="lineno">  905</span>&#160;EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool(<a class="code" href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">isinf</a>)(<span class="keyword">const</span> Eigen::half&amp; h) {</div>
<div class="line"><a name="l00906"></a><span class="lineno">  906</span>&#160;  <span class="keywordflow">return</span> (half_impl::isinf)(h);</div>
<div class="line"><a name="l00907"></a><span class="lineno">  907</span>&#160;}</div>
<div class="line"><a name="l00908"></a><span class="lineno">  908</span>&#160; </div>
<div class="line"><a name="l00909"></a><span class="lineno">  909</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00910"></a><span class="lineno">  910</span>&#160;EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool(<a class="code" href="namespaceEigen.html#aba24ec81dec745a00b7f33adead89811">isfinite</a>)(<span class="keyword">const</span> Eigen::half&amp; h) {</div>
<div class="line"><a name="l00911"></a><span class="lineno">  911</span>&#160;  <span class="keywordflow">return</span> (half_impl::isfinite)(h);</div>
<div class="line"><a name="l00912"></a><span class="lineno">  912</span>&#160;}</div>
<div class="line"><a name="l00913"></a><span class="lineno">  913</span>&#160; </div>
<div class="line"><a name="l00914"></a><span class="lineno">  914</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00915"></a><span class="lineno">  915</span>&#160; </div>
<div class="line"><a name="l00916"></a><span class="lineno">  916</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00917"></a><span class="lineno">  917</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bit_cast&lt;Eigen::half, uint16_t&gt;(<span class="keyword">const</span> uint16_t&amp; src) {</div>
<div class="line"><a name="l00918"></a><span class="lineno">  918</span>&#160;  <span class="keywordflow">return</span> Eigen::half(Eigen::half_impl::raw_uint16_to_half(src));</div>
<div class="line"><a name="l00919"></a><span class="lineno">  919</span>&#160;}</div>
<div class="line"><a name="l00920"></a><span class="lineno">  920</span>&#160; </div>
<div class="line"><a name="l00921"></a><span class="lineno">  921</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l00922"></a><span class="lineno">  922</span>&#160;EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC uint16_t bit_cast&lt;uint16_t, Eigen::half&gt;(<span class="keyword">const</span> Eigen::half&amp; src) {</div>
<div class="line"><a name="l00923"></a><span class="lineno">  923</span>&#160;  <span class="keywordflow">return</span> Eigen::half_impl::raw_half_as_uint16(src);</div>
<div class="line"><a name="l00924"></a><span class="lineno">  924</span>&#160;}</div>
<div class="line"><a name="l00925"></a><span class="lineno">  925</span>&#160; </div>
<div class="line"><a name="l00926"></a><span class="lineno">  926</span>&#160;}  <span class="comment">// namespace numext</span></div>
<div class="line"><a name="l00927"></a><span class="lineno">  927</span>&#160;}  <span class="comment">// namespace Eigen</span></div>
<div class="line"><a name="l00928"></a><span class="lineno">  928</span>&#160; </div>
<div class="line"><a name="l00929"></a><span class="lineno">  929</span>&#160;<span class="comment">// Add the missing shfl* intrinsics.</span></div>
<div class="line"><a name="l00930"></a><span class="lineno">  930</span>&#160;<span class="comment">// The __shfl* functions are only valid on HIP or _CUDA_ARCH_ &gt;= 300.</span></div>
<div class="line"><a name="l00931"></a><span class="lineno">  931</span>&#160;<span class="comment">//   CUDA defines them for (__CUDA_ARCH__ &gt;= 300 || !defined(__CUDA_ARCH__))</span></div>
<div class="line"><a name="l00932"></a><span class="lineno">  932</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00933"></a><span class="lineno">  933</span>&#160;<span class="comment">// HIP and CUDA prior to SDK 9.0 define</span></div>
<div class="line"><a name="l00934"></a><span class="lineno">  934</span>&#160;<span class="comment">//    __shfl, __shfl_up, __shfl_down, __shfl_xor for int and float</span></div>
<div class="line"><a name="l00935"></a><span class="lineno">  935</span>&#160;<span class="comment">// CUDA since 9.0 deprecates those and instead defines</span></div>
<div class="line"><a name="l00936"></a><span class="lineno">  936</span>&#160;<span class="comment">//    __shfl_sync, __shfl_up_sync, __shfl_down_sync, __shfl_xor_sync,</span></div>
<div class="line"><a name="l00937"></a><span class="lineno">  937</span>&#160;<span class="comment">//    with native support for __half and __nv_bfloat16</span></div>
<div class="line"><a name="l00938"></a><span class="lineno">  938</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00939"></a><span class="lineno">  939</span>&#160;<span class="comment">// Note that the following are __device__ - only functions.</span></div>
<div class="line"><a name="l00940"></a><span class="lineno">  940</span>&#160;<span class="preprocessor">#if (defined(EIGEN_CUDACC) &amp;&amp; (!defined(EIGEN_CUDA_ARCH) || EIGEN_CUDA_ARCH &gt;= 300)) \</span></div>
<div class="line"><a name="l00941"></a><span class="lineno">  941</span>&#160;<span class="preprocessor">    || defined(EIGEN_HIPCC)</span></div>
<div class="line"><a name="l00942"></a><span class="lineno">  942</span>&#160; </div>
<div class="line"><a name="l00943"></a><span class="lineno">  943</span>&#160;<span class="preprocessor">#if defined(EIGEN_HAS_CUDA_FP16) &amp;&amp; EIGEN_CUDA_SDK_VER &gt;= 90000</span></div>
<div class="line"><a name="l00944"></a><span class="lineno">  944</span>&#160; </div>
<div class="line"><a name="l00945"></a><span class="lineno">  945</span>&#160;__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_sync(<span class="keywordtype">unsigned</span> mask, Eigen::half var, <span class="keywordtype">int</span> srcLane, <span class="keywordtype">int</span> width=warpSize) {</div>
<div class="line"><a name="l00946"></a><span class="lineno">  946</span>&#160;  <span class="keyword">const</span> __half h = var;</div>
<div class="line"><a name="l00947"></a><span class="lineno">  947</span>&#160;  <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>Eigen::half<span class="keyword">&gt;</span>(__shfl_sync(mask, h, srcLane, width));</div>
<div class="line"><a name="l00948"></a><span class="lineno">  948</span>&#160;}</div>
<div class="line"><a name="l00949"></a><span class="lineno">  949</span>&#160; </div>
<div class="line"><a name="l00950"></a><span class="lineno">  950</span>&#160;__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_up_sync(<span class="keywordtype">unsigned</span> mask, Eigen::half var, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> delta, <span class="keywordtype">int</span> width=warpSize) {</div>
<div class="line"><a name="l00951"></a><span class="lineno">  951</span>&#160;  <span class="keyword">const</span> __half h = var;</div>
<div class="line"><a name="l00952"></a><span class="lineno">  952</span>&#160;  <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>Eigen::half<span class="keyword">&gt;</span>(__shfl_up_sync(mask, h, delta, width));</div>
<div class="line"><a name="l00953"></a><span class="lineno">  953</span>&#160;}</div>
<div class="line"><a name="l00954"></a><span class="lineno">  954</span>&#160; </div>
<div class="line"><a name="l00955"></a><span class="lineno">  955</span>&#160;__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_down_sync(<span class="keywordtype">unsigned</span> mask, Eigen::half var, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> delta, <span class="keywordtype">int</span> width=warpSize) {</div>
<div class="line"><a name="l00956"></a><span class="lineno">  956</span>&#160;  <span class="keyword">const</span> __half h = var;</div>
<div class="line"><a name="l00957"></a><span class="lineno">  957</span>&#160;  <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>Eigen::half<span class="keyword">&gt;</span>(__shfl_down_sync(mask, h, delta, width));</div>
<div class="line"><a name="l00958"></a><span class="lineno">  958</span>&#160;}</div>
<div class="line"><a name="l00959"></a><span class="lineno">  959</span>&#160; </div>
<div class="line"><a name="l00960"></a><span class="lineno">  960</span>&#160;__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor_sync(<span class="keywordtype">unsigned</span> mask, Eigen::half var, <span class="keywordtype">int</span> laneMask, <span class="keywordtype">int</span> width=warpSize) {</div>
<div class="line"><a name="l00961"></a><span class="lineno">  961</span>&#160;  <span class="keyword">const</span> __half h = var;</div>
<div class="line"><a name="l00962"></a><span class="lineno">  962</span>&#160;  <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>Eigen::half<span class="keyword">&gt;</span>(__shfl_xor_sync(mask, h, laneMask, width));</div>
<div class="line"><a name="l00963"></a><span class="lineno">  963</span>&#160;}</div>
<div class="line"><a name="l00964"></a><span class="lineno">  964</span>&#160; </div>
<div class="line"><a name="l00965"></a><span class="lineno">  965</span>&#160;<span class="preprocessor">#else </span><span class="comment">// HIP or CUDA SDK &lt; 9.0</span></div>
<div class="line"><a name="l00966"></a><span class="lineno">  966</span>&#160; </div>
<div class="line"><a name="l00967"></a><span class="lineno">  967</span>&#160;__device__ EIGEN_STRONG_INLINE Eigen::half __shfl(Eigen::half var, <span class="keywordtype">int</span> srcLane, <span class="keywordtype">int</span> width=warpSize) {</div>
<div class="line"><a name="l00968"></a><span class="lineno">  968</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> ivar = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(Eigen::numext::bit_cast&lt;Eigen::numext::uint16_t&gt;(var));</div>
<div class="line"><a name="l00969"></a><span class="lineno">  969</span>&#160;  <span class="keywordflow">return</span> Eigen::numext::bit_cast&lt;Eigen::half&gt;(<span class="keyword">static_cast&lt;</span>Eigen::numext::uint16_t<span class="keyword">&gt;</span>(__shfl(ivar, srcLane, width)));</div>
<div class="line"><a name="l00970"></a><span class="lineno">  970</span>&#160;}</div>
<div class="line"><a name="l00971"></a><span class="lineno">  971</span>&#160; </div>
<div class="line"><a name="l00972"></a><span class="lineno">  972</span>&#160;__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_up(Eigen::half var, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> delta, <span class="keywordtype">int</span> width=warpSize) {</div>
<div class="line"><a name="l00973"></a><span class="lineno">  973</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> ivar = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(Eigen::numext::bit_cast&lt;Eigen::numext::uint16_t&gt;(var));</div>
<div class="line"><a name="l00974"></a><span class="lineno">  974</span>&#160;  <span class="keywordflow">return</span> Eigen::numext::bit_cast&lt;Eigen::half&gt;(<span class="keyword">static_cast&lt;</span>Eigen::numext::uint16_t<span class="keyword">&gt;</span>(__shfl_up(ivar, delta, width)));</div>
<div class="line"><a name="l00975"></a><span class="lineno">  975</span>&#160;}</div>
<div class="line"><a name="l00976"></a><span class="lineno">  976</span>&#160; </div>
<div class="line"><a name="l00977"></a><span class="lineno">  977</span>&#160;__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_down(Eigen::half var, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> delta, <span class="keywordtype">int</span> width=warpSize) {</div>
<div class="line"><a name="l00978"></a><span class="lineno">  978</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> ivar = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(Eigen::numext::bit_cast&lt;Eigen::numext::uint16_t&gt;(var));</div>
<div class="line"><a name="l00979"></a><span class="lineno">  979</span>&#160;  <span class="keywordflow">return</span> Eigen::numext::bit_cast&lt;Eigen::half&gt;(<span class="keyword">static_cast&lt;</span>Eigen::numext::uint16_t<span class="keyword">&gt;</span>(__shfl_down(ivar, delta, width)));</div>
<div class="line"><a name="l00980"></a><span class="lineno">  980</span>&#160;}</div>
<div class="line"><a name="l00981"></a><span class="lineno">  981</span>&#160; </div>
<div class="line"><a name="l00982"></a><span class="lineno">  982</span>&#160;__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor(Eigen::half var, <span class="keywordtype">int</span> laneMask, <span class="keywordtype">int</span> width=warpSize) {</div>
<div class="line"><a name="l00983"></a><span class="lineno">  983</span>&#160;  <span class="keyword">const</span> <span class="keywordtype">int</span> ivar = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(Eigen::numext::bit_cast&lt;Eigen::numext::uint16_t&gt;(var));</div>
<div class="line"><a name="l00984"></a><span class="lineno">  984</span>&#160;  <span class="keywordflow">return</span> Eigen::numext::bit_cast&lt;Eigen::half&gt;(<span class="keyword">static_cast&lt;</span>Eigen::numext::uint16_t<span class="keyword">&gt;</span>(__shfl_xor(ivar, laneMask, width)));</div>
<div class="line"><a name="l00985"></a><span class="lineno">  985</span>&#160;}</div>
<div class="line"><a name="l00986"></a><span class="lineno">  986</span>&#160; </div>
<div class="line"><a name="l00987"></a><span class="lineno">  987</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// HIP vs CUDA</span></div>
<div class="line"><a name="l00988"></a><span class="lineno">  988</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// __shfl*</span></div>
<div class="line"><a name="l00989"></a><span class="lineno">  989</span>&#160; </div>
<div class="line"><a name="l00990"></a><span class="lineno">  990</span>&#160;<span class="comment">// ldg() has an overload for __half_raw, but we also need one for Eigen::half.</span></div>
<div class="line"><a name="l00991"></a><span class="lineno">  991</span>&#160;<span class="preprocessor">#if (defined(EIGEN_CUDACC) &amp;&amp; (!defined(EIGEN_CUDA_ARCH) || EIGEN_CUDA_ARCH &gt;= 350)) \</span></div>
<div class="line"><a name="l00992"></a><span class="lineno">  992</span>&#160;<span class="preprocessor">    || defined(EIGEN_HIPCC)</span></div>
<div class="line"><a name="l00993"></a><span class="lineno">  993</span>&#160;EIGEN_STRONG_INLINE __device__ Eigen::half __ldg(<span class="keyword">const</span> Eigen::half* ptr) {</div>
<div class="line"><a name="l00994"></a><span class="lineno">  994</span>&#160;  <span class="keywordflow">return</span> Eigen::half_impl::raw_uint16_to_half(__ldg(<span class="keyword">reinterpret_cast&lt;</span><span class="keyword">const </span>Eigen::numext::uint16_t*<span class="keyword">&gt;</span>(ptr)));</div>
<div class="line"><a name="l00995"></a><span class="lineno">  995</span>&#160;}</div>
<div class="line"><a name="l00996"></a><span class="lineno">  996</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// __ldg</span></div>
<div class="line"><a name="l00997"></a><span class="lineno">  997</span>&#160; </div>
<div class="line"><a name="l00998"></a><span class="lineno">  998</span>&#160;<span class="preprocessor">#if EIGEN_HAS_STD_HASH</span></div>
<div class="line"><a name="l00999"></a><span class="lineno">  999</span>&#160;<span class="keyword">namespace </span>std {</div>
<div class="line"><a name="l01000"></a><span class="lineno"> 1000</span>&#160;<span class="keyword">template</span> &lt;&gt;</div>
<div class="line"><a name="l01001"></a><span class="lineno"> 1001</span>&#160;<span class="keyword">struct </span>hash&lt;<a class="code" href="namespaceEigen.html">Eigen</a>::half&gt; {</div>
<div class="line"><a name="l01002"></a><span class="lineno"> 1002</span>&#160;  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::size_t operator()(<span class="keyword">const</span> Eigen::half&amp; a)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l01003"></a><span class="lineno"> 1003</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>std::size_t<span class="keyword">&gt;</span>(Eigen::numext::bit_cast&lt;Eigen::numext::uint16_t&gt;(a));</div>
<div class="line"><a name="l01004"></a><span class="lineno"> 1004</span>&#160;  }</div>
<div class="line"><a name="l01005"></a><span class="lineno"> 1005</span>&#160;};</div>
<div class="line"><a name="l01006"></a><span class="lineno"> 1006</span>&#160;} <span class="comment">// end namespace std</span></div>
<div class="line"><a name="l01007"></a><span class="lineno"> 1007</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01008"></a><span class="lineno"> 1008</span>&#160; </div>
<div class="line"><a name="l01009"></a><span class="lineno"> 1009</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_HALF_H</span></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a0110c233d357169fd58fdf5656992a98"><div class="ttname"><a href="namespaceEigen.html#a0110c233d357169fd58fdf5656992a98">Eigen::tanh</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_tanh_op&lt; typename Derived::Scalar &gt;, const Derived &gt; tanh(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a0211fe61b9e390dfd8ca213fe9c7fca3"><div class="ttname"><a href="namespaceEigen.html#a0211fe61b9e390dfd8ca213fe9c7fca3">Eigen::rint</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_rint_op&lt; typename Derived::Scalar &gt;, const Derived &gt; rint(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a1f1103712e337c4c96a05f949637a4c8"><div class="ttname"><a href="namespaceEigen.html#a1f1103712e337c4c96a05f949637a4c8">Eigen::isinf</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_isinf_op&lt; typename Derived::Scalar &gt;, const Derived &gt; isinf(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a25256faeec3ffd0f3615a0e1e45dfb14"><div class="ttname"><a href="namespaceEigen.html#a25256faeec3ffd0f3615a0e1e45dfb14">Eigen::log10</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_log10_op&lt; typename Derived::Scalar &gt;, const Derived &gt; log10(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a3bc116a6243f38c22f851581aa7b521a"><div class="ttname"><a href="namespaceEigen.html#a3bc116a6243f38c22f851581aa7b521a">Eigen::tan</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_tan_op&lt; typename Derived::Scalar &gt;, const Derived &gt; tan(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a3fe3a136370fefae062591304c6a7ebd"><div class="ttname"><a href="namespaceEigen.html#a3fe3a136370fefae062591304c6a7ebd">Eigen::acos</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_acos_op&lt; typename Derived::Scalar &gt;, const Derived &gt; acos(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_a6c5c246b877ac331495d21e7a5d51616"><div class="ttname"><a href="namespaceEigen.html#a6c5c246b877ac331495d21e7a5d51616">Eigen::asin</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_asin_op&lt; typename Derived::Scalar &gt;, const Derived &gt; asin(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a831e88e0403a42d0dfb328d8acd3e56f"><div class="ttname"><a href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">Eigen::sign</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sign_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sign(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_a9723b3ff0f2c99fe1081e3eb14380d4c"><div class="ttname"><a href="namespaceEigen.html#a9723b3ff0f2c99fe1081e3eb14380d4c">Eigen::operator*</a></div><div class="ttdeci">const Product&lt; MatrixDerived, PermutationDerived, AliasFreeProduct &gt; operator*(const MatrixBase&lt; MatrixDerived &gt; &amp;matrix, const PermutationBase&lt; PermutationDerived &gt; &amp;permutation)</div><div class="ttdef"><b>Definition:</b> PermutationMatrix.h:517</div></div>
<div class="ttc" id="anamespaceEigen_html_a99adfc5178f3fd5488304284388b2a10"><div class="ttname"><a href="namespaceEigen.html#a99adfc5178f3fd5488304284388b2a10">Eigen::isnan</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_isnan_op&lt; typename Derived::Scalar &gt;, const Derived &gt; isnan(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_aa73e38be0689a463ae14141b9cf89c35"><div class="ttname"><a href="namespaceEigen.html#aa73e38be0689a463ae14141b9cf89c35">Eigen::ceil</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_ceil_op&lt; typename Derived::Scalar &gt;, const Derived &gt; ceil(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_aba24ec81dec745a00b7f33adead89811"><div class="ttname"><a href="namespaceEigen.html#aba24ec81dec745a00b7f33adead89811">Eigen::isfinite</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_isfinite_op&lt; typename Derived::Scalar &gt;, const Derived &gt; isfinite(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_abf03d773a87830bc7fde51bcd94c89a0"><div class="ttname"><a href="namespaceEigen.html#abf03d773a87830bc7fde51bcd94c89a0">Eigen::floor</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_floor_op&lt; typename Derived::Scalar &gt;, const Derived &gt; floor(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ac5c8a2cded6b59628f2de04f24d2fff4"><div class="ttname"><a href="namespaceEigen.html#ac5c8a2cded6b59628f2de04f24d2fff4">Eigen::log1p</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_log1p_op&lt; typename Derived::Scalar &gt;, const Derived &gt; log1p(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ac74dc920119b1eba45e9218d9f402afc"><div class="ttname"><a href="namespaceEigen.html#ac74dc920119b1eba45e9218d9f402afc">Eigen::real</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_real_op&lt; typename Derived::Scalar &gt;, const Derived &gt; real(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad01d50a42869218f1d54af13f71517a6"><div class="ttname"><a href="namespaceEigen.html#ad01d50a42869218f1d54af13f71517a6">Eigen::cos</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_cos_op&lt; typename Derived::Scalar &gt;, const Derived &gt; cos(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad2d0241ffaaa3b0b04ec70b59ab066d4"><div class="ttname"><a href="namespaceEigen.html#ad2d0241ffaaa3b0b04ec70b59ab066d4">Eigen::log2</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_log2_op&lt; typename Derived::Scalar &gt;, const Derived &gt; log2(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ad9eaa98e8016ef17024a18a2f3e5bef3"><div class="ttname"><a href="namespaceEigen.html#ad9eaa98e8016ef17024a18a2f3e5bef3">Eigen::round</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_round_op&lt; typename Derived::Scalar &gt;, const Derived &gt; round(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae491aecf7dab66ac7e11008c5766694d"><div class="ttname"><a href="namespaceEigen.html#ae491aecf7dab66ac7e11008c5766694d">Eigen::exp</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_exp_op&lt; typename Derived::Scalar &gt;, const Derived &gt; exp(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae6e8ad270ff41c088d7651567594f796"><div class="ttname"><a href="namespaceEigen.html#ae6e8ad270ff41c088d7651567594f796">Eigen::sin</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sin_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sin(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae7cb2544e4e745bc0067fe793e3f2f81"><div class="ttname"><a href="namespaceEigen.html#ae7cb2544e4e745bc0067fe793e3f2f81">Eigen::expm1</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_expm1_op&lt; typename Derived::Scalar &gt;, const Derived &gt; expm1(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae8bb75ba4f5f30a7571146dbfa653c6d"><div class="ttname"><a href="namespaceEigen.html#ae8bb75ba4f5f30a7571146dbfa653c6d">Eigen::log</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_log_op&lt; typename Derived::Scalar &gt;, const Derived &gt; log(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af4f536e8ea56702e63088efb3706d1f0"><div class="ttname"><a href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">Eigen::sqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
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